{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Practical Statistics for Data Scientists (R)\n",
    "# Chapter 3. Statistial Experiments and Significance Testing\n",
    "> (c) 2019 Peter C. Bruce, Andrew Bruce, Peter Gedeck"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import required R packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:04.064578Z",
     "iopub.status.busy": "2022-04-26T20:06:04.062029Z",
     "iopub.status.idle": "2022-04-26T20:06:04.088759Z",
     "shell.execute_reply": "2022-04-26T20:06:04.086943Z"
    }
   },
   "outputs": [],
   "source": [
    "# lmPerm is available from CRAN\n",
    "# conda install r-devtools\n",
    "# devtools::install_github('mtorchiano/lmPerm')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:04.122403Z",
     "iopub.status.busy": "2022-04-26T20:06:04.092145Z",
     "iopub.status.idle": "2022-04-26T20:06:04.444302Z",
     "shell.execute_reply": "2022-04-26T20:06:04.442833Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "“package ‘dplyr’ was built under R version 4.1.2”\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "Attaching package: ‘dplyr’\n",
      "\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "The following objects are masked from ‘package:stats’:\n",
      "\n",
      "    filter, lag\n",
      "\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "The following objects are masked from ‘package:base’:\n",
      "\n",
      "    intersect, setdiff, setequal, union\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(dplyr)\n",
    "library(lmPerm)\n",
    "library(pwr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define paths to data sets. If you don't keep your data in the same directory as the code, adapt the path names."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:04.448609Z",
     "iopub.status.busy": "2022-04-26T20:06:04.447518Z",
     "iopub.status.idle": "2022-04-26T20:06:04.482037Z",
     "shell.execute_reply": "2022-04-26T20:06:04.479619Z"
    }
   },
   "outputs": [],
   "source": [
    "PSDS_PATH <- file.path(dirname(dirname(getwd())))\n",
    "\n",
    "\n",
    "session_times <- read.csv(file.path(PSDS_PATH, 'data', 'web_page_data.csv'))\n",
    "session_times[,2] <- session_times[,2] * 100\n",
    "four_sessions  <- read.csv(file.path(PSDS_PATH, 'data', 'four_sessions.csv'))\n",
    "click_rate <-  read.csv(file.path(PSDS_PATH, 'data', 'click_rates.csv'))\n",
    "imanishi <-  read.csv(file.path(PSDS_PATH, 'data', 'imanishi_data.csv'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Resampling\n",
    "## Example: Web Stickiness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:04.486807Z",
     "iopub.status.busy": "2022-04-26T20:06:04.485110Z",
     "iopub.status.idle": "2022-04-26T20:06:04.725431Z",
     "shell.execute_reply": "2022-04-26T20:06:04.722677Z"
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAC9FBMVEUAAAABAQECAgIDAwME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\nRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph <- ggplot(session_times, aes(x=Page, y=Time)) + \n",
    "  geom_boxplot() +\n",
    "  labs(y='Time (in seconds)') + \n",
    "  theme_bw()\n",
    "graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:04.730041Z",
     "iopub.status.busy": "2022-04-26T20:06:04.728837Z",
     "iopub.status.idle": "2022-04-26T20:06:04.748111Z",
     "shell.execute_reply": "2022-04-26T20:06:04.746789Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "35.6666666666667"
      ],
      "text/latex": [
       "35.6666666666667"
      ],
      "text/markdown": [
       "35.6666666666667"
      ],
      "text/plain": [
       "[1] 35.66667"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean_a <- mean(session_times[session_times['Page'] == 'Page A', 'Time'])\n",
    "mean_b <- mean(session_times[session_times['Page'] == 'Page B', 'Time'])\n",
    "mean_b - mean_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:04.752347Z",
     "iopub.status.busy": "2022-04-26T20:06:04.751256Z",
     "iopub.status.idle": "2022-04-26T20:06:04.761322Z",
     "shell.execute_reply": "2022-04-26T20:06:04.759527Z"
    }
   },
   "outputs": [],
   "source": [
    "## Permutation test example with stickiness\n",
    "perm_fun <- function(x, nA, nB)\n",
    "{\n",
    "  n <- nA + nB\n",
    "  idx_b <- sample(1:n, nB)\n",
    "  idx_a <- setdiff(1:n, idx_b)\n",
    "  mean_diff <- mean(x[idx_b]) - mean(x[idx_a])\n",
    "  return(mean_diff)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:04.768118Z",
     "iopub.status.busy": "2022-04-26T20:06:04.766468Z",
     "iopub.status.idle": "2022-04-26T20:06:04.882911Z",
     "shell.execute_reply": "2022-04-26T20:06:04.881629Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAADAFBMVEUAAAABAQECAgIDAwME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\nQmCC",
      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(1)\n",
    "perm_diffs <- rep(0, 1000)\n",
    "for (i in 1:1000) {\n",
    "  perm_diffs[i] = perm_fun(session_times[, 'Time'], 21, 15)\n",
    "}\n",
    "par(mar=c(4,4,1,0)+.1)\n",
    "hist(perm_diffs, xlab='Session time differences (in seconds)', main='')\n",
    "abline(v=mean_b - mean_a, lty=2, lwd=1.5)\n",
    "text('  Observed\\n  difference', x=mean_b - mean_a,  y=par()$usr[4]-20, adj=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:04.887006Z",
     "iopub.status.busy": "2022-04-26T20:06:04.885902Z",
     "iopub.status.idle": "2022-04-26T20:06:04.897203Z",
     "shell.execute_reply": "2022-04-26T20:06:04.895875Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.141"
      ],
      "text/latex": [
       "0.141"
      ],
      "text/markdown": [
       "0.141"
      ],
      "text/plain": [
       "[1] 0.141"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(perm_diffs > (mean_b - mean_a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Statistical Significance and P-Values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:04.901489Z",
     "iopub.status.busy": "2022-04-26T20:06:04.900397Z",
     "iopub.status.idle": "2022-04-26T20:06:13.059009Z",
     "shell.execute_reply": "2022-04-26T20:06:13.057719Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAC+lBMVEUAAAABAQECAgIDAwME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\n",
      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "obs_pct_diff <- 100 * (200 / 23739 - 182 / 22588)\n",
    "conversion <- c(rep(0, 45945), rep(1, 382))\n",
    "perm_diffs <- rep(0, 1000)\n",
    "for (i in 1:1000) {\n",
    "  perm_diffs[i] = 100 * perm_fun(conversion, 23739, 22588)\n",
    "}\n",
    "\n",
    "hist(perm_diffs, xlab='Conversion rate (percent)', main='')\n",
    "abline(v=obs_pct_diff, lty=2, lwd=1.5)\n",
    "text('   Observed\\n   difference', x=obs_pct_diff,  y=par()$usr[4]-20, adj=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:13.062771Z",
     "iopub.status.busy": "2022-04-26T20:06:13.061764Z",
     "iopub.status.idle": "2022-04-26T20:06:13.072903Z",
     "shell.execute_reply": "2022-04-26T20:06:13.071695Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.0367579118205928"
      ],
      "text/latex": [
       "0.0367579118205928"
      ],
      "text/markdown": [
       "0.0367579118205928"
      ],
      "text/plain": [
       "[1] 0.03675791"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Obbserved difference\n",
    "obs_pct_diff"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## P-Value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:13.076811Z",
     "iopub.status.busy": "2022-04-26T20:06:13.075830Z",
     "iopub.status.idle": "2022-04-26T20:06:13.086258Z",
     "shell.execute_reply": "2022-04-26T20:06:13.084986Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.34"
      ],
      "text/latex": [
       "0.34"
      ],
      "text/markdown": [
       "0.34"
      ],
      "text/plain": [
       "[1] 0.34"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean(perm_diffs > obs_pct_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:13.090430Z",
     "iopub.status.busy": "2022-04-26T20:06:13.089361Z",
     "iopub.status.idle": "2022-04-26T20:06:13.101838Z",
     "shell.execute_reply": "2022-04-26T20:06:13.100608Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\t2-sample test for equality of proportions with continuity correction\n",
       "\n",
       "data:  c(200, 182) out of c(23739, 22588)\n",
       "X-squared = 0.14893, df = 1, p-value = 0.3498\n",
       "alternative hypothesis: greater\n",
       "95 percent confidence interval:\n",
       " -0.001057439  1.000000000\n",
       "sample estimates:\n",
       "     prop 1      prop 2 \n",
       "0.008424955 0.008057376 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prop.test(x=c(200,182), n=c(23739,22588), alternative='greater')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# t-Tests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:13.106103Z",
     "iopub.status.busy": "2022-04-26T20:06:13.104942Z",
     "iopub.status.idle": "2022-04-26T20:06:13.121956Z",
     "shell.execute_reply": "2022-04-26T20:06:13.120595Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tWelch Two Sample t-test\n",
       "\n",
       "data:  Time by Page\n",
       "t = -1.0983, df = 27.693, p-value = 0.1408\n",
       "alternative hypothesis: true difference in means between group Page A and group Page B is less than 0\n",
       "95 percent confidence interval:\n",
       "     -Inf 19.59674\n",
       "sample estimates:\n",
       "mean in group Page A mean in group Page B \n",
       "            126.3333             162.0000 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t.test(Time ~ Page, data=session_times, alternative='less')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ANOVA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:13.126242Z",
     "iopub.status.busy": "2022-04-26T20:06:13.125112Z",
     "iopub.status.idle": "2022-04-26T20:06:13.293064Z",
     "shell.execute_reply": "2022-04-26T20:06:13.291782Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAC91BMVEUAAAABAQECAgIDAwME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\n",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "graph <- ggplot(four_sessions, aes(x=Page, y=Time)) + \n",
    "  geom_boxplot() +\n",
    "  labs(y='Time (in seconds)') +\n",
    "  theme_bw()\n",
    "graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:13.297265Z",
     "iopub.status.busy": "2022-04-26T20:06:13.296194Z",
     "iopub.status.idle": "2022-04-26T20:06:13.325311Z",
     "shell.execute_reply": "2022-04-26T20:06:13.323988Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Settings:  unique SS \"\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Component 1 :\n",
       "            Df R Sum Sq R Mean Sq Iter Pr(Prob)  \n",
       "Page1        3    831.4    277.13 5000   0.0772 .\n",
       "Residuals   16   1618.4    101.15                \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(lmPerm)\n",
    "summary(aovp(Time ~ Page, data=four_sessions))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## F-Statistic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:13.329676Z",
     "iopub.status.busy": "2022-04-26T20:06:13.328584Z",
     "iopub.status.idle": "2022-04-26T20:06:13.343722Z",
     "shell.execute_reply": "2022-04-26T20:06:13.342424Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "            Df Sum Sq Mean Sq F value Pr(>F)  \n",
       "Page         3  831.4   277.1    2.74 0.0776 .\n",
       "Residuals   16 1618.4   101.2                 \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(aov(Time ~ Page, data=four_sessions))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chi-Square Test\n",
    "## Chi-Square Test: A Resampling Approach"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:13.348049Z",
     "iopub.status.busy": "2022-04-26T20:06:13.346996Z",
     "iopub.status.idle": "2022-04-26T20:06:13.362610Z",
     "shell.execute_reply": "2022-04-26T20:06:13.361315Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPearson's Chi-squared test with simulated p-value (based on 2000\n",
       "\treplicates)\n",
       "\n",
       "data:  clicks\n",
       "X-squared = 1.6659, df = NA, p-value = 0.4793\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "clicks <- matrix(click_rate$Rate, nrow=3, ncol=2, byrow=TRUE)\n",
    "dimnames(clicks) <- list(unique(click_rate$Headline), unique(click_rate$Click))\n",
    "\n",
    "chisq.test(clicks, simulate.p.value=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:13.367027Z",
     "iopub.status.busy": "2022-04-26T20:06:13.365842Z",
     "iopub.status.idle": "2022-04-26T20:06:13.381573Z",
     "shell.execute_reply": "2022-04-26T20:06:13.380269Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPearson's Chi-squared test\n",
       "\n",
       "data:  clicks\n",
       "X-squared = 1.6659, df = 2, p-value = 0.4348\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "chisq.test(clicks, simulate.p.value=FALSE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Figure chi-sq distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:13.385996Z",
     "iopub.status.busy": "2022-04-26T20:06:13.384883Z",
     "iopub.status.idle": "2022-04-26T20:06:13.631280Z",
     "shell.execute_reply": "2022-04-26T20:06:13.629935Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAADAFBMVEUAAAABAQECAgIDAwME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\nSUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- seq(1, 30, length=100)\n",
    "chi <- data.frame(df = factor(rep(c(1, 2, 5, 20), rep(100, 4))),\n",
    "                  x = rep(x, 4),\n",
    "                  p = c(dchisq(x, 1), dchisq(x, 2), dchisq(x, 5), dchisq(x, 20)))\n",
    "\n",
    "graph <- ggplot(chi, aes(x=x, y=p)) +\n",
    "  geom_line(aes(linetype=df)) +\n",
    "  geom_text(aes(x=25, y=0.06, label='df=20'), size=2.5) +\n",
    "  geom_text(aes(x=8, y=0.1, label='df=5'), size=2.5) +\n",
    "  geom_text(aes(x=4, y=0.2, label='df=2'), size=2.5) +\n",
    "  geom_text(aes(x=1.5, y=0.05, label='df=1'), size=2.5) +\n",
    "  theme_bw() + theme(legend.position = \"none\") +\n",
    "  labs(x='Value of chi-square statistic', y='Probability')\n",
    "graph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fisher's Exact Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:13.635440Z",
     "iopub.status.busy": "2022-04-26T20:06:13.634373Z",
     "iopub.status.idle": "2022-04-26T20:06:13.646220Z",
     "shell.execute_reply": "2022-04-26T20:06:13.644941Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tFisher's Exact Test for Count Data\n",
       "\n",
       "data:  clicks\n",
       "p-value = 0.4824\n",
       "alternative hypothesis: two.sided\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fisher.test(clicks)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scientific Fraud"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:13.650347Z",
     "iopub.status.busy": "2022-04-26T20:06:13.649250Z",
     "iopub.status.idle": "2022-04-26T20:06:13.809090Z",
     "shell.execute_reply": "2022-04-26T20:06:13.807828Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAC5VBMVEUAAAABAQECAgIDAwME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\ngg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Code for Figure 8\n",
    "imanishi$Digit <- factor(imanishi$Digit)\n",
    "\n",
    "graph <- ggplot(imanishi, aes(x=Digit, y=Frequency)) +\n",
    "  geom_bar(stat='identity') +\n",
    "  theme_bw()\n",
    "graph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Power and Sample Size\n",
    "## Sample Size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:13.813232Z",
     "iopub.status.busy": "2022-04-26T20:06:13.812119Z",
     "iopub.status.idle": "2022-04-26T20:06:13.829650Z",
     "shell.execute_reply": "2022-04-26T20:06:13.827923Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "     Difference of proportion power calculation for binomial distribution (arcsine transformation) \n",
       "\n",
       "              h = 0.01029785\n",
       "              n = 116601.7\n",
       "      sig.level = 0.05\n",
       "          power = 0.8\n",
       "    alternative = greater\n",
       "\n",
       "NOTE: same sample sizes\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "effect_size = ES.h(p1=0.0121, p2=0.011)\n",
    "pwr.2p.test(h=effect_size, sig.level=0.05, power=0.8, alternative='greater')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2022-04-26T20:06:13.854493Z",
     "iopub.status.busy": "2022-04-26T20:06:13.852910Z",
     "iopub.status.idle": "2022-04-26T20:06:13.868417Z",
     "shell.execute_reply": "2022-04-26T20:06:13.867141Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "     Difference of proportion power calculation for binomial distribution (arcsine transformation) \n",
       "\n",
       "              h = 0.04746819\n",
       "              n = 5487.731\n",
       "      sig.level = 0.05\n",
       "          power = 0.8\n",
       "    alternative = greater\n",
       "\n",
       "NOTE: same sample sizes\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "effect_size = ES.h(p1=0.0165, p2=0.011)\n",
    "pwr.2p.test(h=effect_size, sig.level=0.05, power=0.8, alternative='greater')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.1.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
